REAL SUBMANIFOLDS OF MAXIMUM COMPLEX TANGENT SPACE AT A CR SINGULAR POINT, IReport as inadecuate




REAL SUBMANIFOLDS OF MAXIMUM COMPLEX TANGENT SPACE AT A CR SINGULAR POINT, I - Download this document for free, or read online. Document in PDF available to download.

1 University of Wisconsin, Department of Mathematics 2 JAD - Laboratoire Jean Alexandre Dieudonné

Abstract : We study a germ of real analytic n-dimensional submanifold of C n that has a complex tangent space of maximal dimension at a CR singularity. Under some assumptions , we show its equivalence to a normal form under a local biholomorphism at the singularity. We also show that if a real submanifold is formally equivalent to a quadric, it is actually holomorphically equivalent to it, if a small divisors condition is satisfied. Finally, we investigate the existence of a complex submanifold of positive dimension in C n that intersects a real submanifold along two totally and real analytic submanifolds that intersect transversally at a possibly non-isolated CR singularity.

Keywords : small divisors linearization Local analytic geometry CR singularity normal form integrability reversible mapping hull of holomorphy.





Author: Xianghong Gong - Laurent Stolovitch -

Source: https://hal.archives-ouvertes.fr/



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